Deck 12: Introduction to Analysis of Variance

Question 1

In an ANOVA,what is represented by the letter T?

A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The total number of scores in the entire study

Answer 1

The sum of the scores in a specific treatment

Question 2

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and X² = 94.For this study,what is $\text { within }$ ?

A)10
B)24
C)34
D)68

Answer 2

24

Question 3

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df within treatment?

A)2
B)11
C)33
D)35

Answer 3

33

Question 4

An analysis of variances produces dfₜₒₜₐₗ = 29 and dfwᵢthᵢn = 27.For this analysis,what is df between ?

A)1
B)2
C)3
D)Cannot be determined without additional information

Question 5

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and X² = 94.For this study,what is $S S _ { \text {between } }$ ?

A)10
B)24
C)34
D)68

Question 6

On average,what value is expected for the F-ratio if the null hypothesis is false?

A)0
B)1.00
C)Between 0 and 1.00
D)Much greater than 1.00

Question 7

An analysis of variance produces SS_Total = 80 and $\text { SSwithin }$ = 30.For this analysis,what is $S S _ { \text {between } }$ ?

A)30
B)50
C)110
D)Cannot be determined without additional information

Question 8

When comparing more than two treatment means,why should you use an analysis of variance instead of using multiple t tests?

A)Using multiple t tests increases the risk of a Type I error.
B)Using multiple t tests increases the risk of a Type II error.
C)The analysis of variance is more likely to detect a treatment effect.
D)There is no advantage to using an analysis of variance instead of multiple t tests.

Question 9

An analysis of variances produces dfₜₒₜₐₗ = 29 and dfwᵢthᵢn = 27.For this analysis,how many treatment conditions are being compared?

A)1
B)2
C)3
D)Cannot be determined without additional information

Question 10

A research study comparing three treatments with n = 5 in each treatment produces T₁ = 5,T₂ = 10,T₃ = 15,with SS₁ = 6,SS₂ = 9,SS₃ = 9,and ΣX² = 94.For this study,what is SSₜₒₜₐₗ?

A)10
B)24
C)34
D)68

Question 11

For an ANOVA comparing three treatment conditions,what is stated by the null hypothesis (H₀)?

A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Question 12

An analysis of variances produces df between = 3 and dfwᵢthᵢn = 24.If each treatment has the same number of participants,then how many participants are in each treatment?

A)6
B)7
C)8
D)9

Question 13

In analysis of variance,what is measured by the MS values?

A)Sample variance
B)Population variance
C)The average distance from one mean to another
D)The total variability for the set of N scores

Question 14

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is dfₜₒₜₐₗ?

A)2
B)11
C)33
D)35

Question 15

In an ANOVA,what is represented by the letter N?

A)The sum of the scores in a specific treatment
B)The sum of the scores in the total research study
C)The number of scores in a specific treatment
D)The total number of scores in the entire study

Question 16

An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment.For this study,what is df between treatment?

A)2
B)11
C)33
D)35

Question 17

In an analysis of variance,differences between participants contribute to which of the following variances?

A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Question 18

On average,what value is expected for the F-ratio if the null hypothesis is true?

A)0
B)1.00
C)k - 1
D)N - k

Question 19

In an analysis of variance,differences caused by treatment effects contribute to which of the following variances?

A)Both between-treatments variance and within-treatments variance
B)Between-treatments variance but not within-treatments variance
C)Within-treatments variance but not between-treatments variance
D)Neither between-treatments variance nor within-treatments variance

Question 20

For an ANOVA comparing three treatment conditions,what is stated by the alternative hypothesis (H₁)?

A)There are no differences between any of the population means.
B)At least one of the three population means is different from another mean.
C)All three of the population means are different from each other.
D)None of the other choices is correct.

Question 21

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment.Note that several values are missing in the table.What is the missing value for MS_within?
$\begin{array}{lcccc}\text { Source } & S S & d f & M S & \\\hline \text { Between } & 30 & \mathrm{xx} & \mathrm{xx} & F=\mathrm{xx} \\\text { Within } & \mathrm{xx} & \mathrm{xx} & \mathrm{xx} & \\\text { Total } & 62 & \mathrm{xx} & &\end{array}$

A)2
B)16
C)32
D)48

Question 22

An analysis of variance produces $S S _ { \text {between } }$ = 30, $\text { SSwithin }$ = 60,and an F-ratio with df = 2,15.For this analysis,what is the F-ratio?

A)30/60 = 0.50
B)60/30 = 2.00
C)15/4 = 3.75
D)4/15 = 0.27

Question 23

A researcher reports an F-ratio with df = 1,24 for an independent-measures experiment.If all the treatments had the same number of participants,then how many individuals were in each treatment?

A)11
B)12
C)13
D)14

Question 24

An analysis of variance produces $S S _ { \text {between } }$ = 40 and t $M S _ { \text {between } }$ = 20.In this analysis,how many treatment conditions are being compared?

A)2
B)3
C)4
D)20

Question 25

An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment.If all three treatments have the same total,T₁ = T₂ = T₃,what is $S S _ { \text {between } }$ ?

A)0
B)1.00
C)10
D)Cannot be determined from the information given

Question 26

An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.For this study,the three samples have SS₁ = 10,SS₂ = 20,and SS₃ = 15.What value would be obtained for MSwᵢthᵢn?

A)45/14
B)45/12
C)10/2
D)10/3

Question 27

Which of the following is expected if the null hypothesis is true for an analysis of variance?

A) $S S _ { \text {between } }$ should be about the same size as SStotal
B) $S S _ { \text {between } }$ should be about the same size as $\text { SSwithin }$
C)MSbetween should be about the same size as MStotal
D)MSbetween should be about the same size as MSwithin

Question 28

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS2 to 100?

Sample Data
$$\begin{array} { l c } M _ { 1 } = 15 & M _ { 2 } = 25 \\S S _ { 1 } = 90 & S S _ { 2 } = 70\end{array}$$

A)Increase $\text { SSwithin }$ and increase the F-ratio
B)Increase $\text { SSwithin }$ and decrease the F-ratio
C)Decrease $\text { SSwithin }$ and increase the F-ratio
D)Decrease $\text { SSwithin }$ and decrease the F-ratio

Question 29

For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment,what is the critical value for the F-ratio using α = .05?

A)3.88
B)3.49
C)3.74
D)3.34

Question 30

A researcher uses analysis of variance to test for mean differences among three treatments with a sample of n = 12 in each treatment.The F-ratio for this analysis would have what df values?

A)2, 11
B)2, 33
C)2, 35
D)2, 36

Question 31

The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 7 participants in each treatment.Note that several values are missing in the table.What is the missing value for MS beetween? $$\begin{array} { l l l r l } \text { Source } & S S & d f & M S & \\\hline \text { Between } & 20 & \mathrm { xx } & \mathrm { xx } & F = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & 2 & \\\text { Total } & \mathrm { xx } & \mathrm { xx } & &\end{array}$$

A)2
B)5
C)10
D)40

Question 32

In an analysis of variance,which of the following is determined by the size of the sample mean differences?

A) $S S _ { \text {between } }$
B) $\text { SSwithin }$
C) $d f _ { \text {between } }$
D) $d f _ { \text {within } }$

Question 33

If an analysis of variance is used for the following data,what would be the effect of changing the value of M1 to 20?

A)Increase $S S _ { \text {between } }$ and increase the F-ratio
B)Increase $S S _ { \text {between } }$ and decrease the F-ratio
C)Decrease $S S _ { \text {between } }$ and increase the F-ratio
D)Decrease $S S _ { \text {between } }$ and decrease the F-ratio

Question 34

The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment.Note that several values are missing in the table.What is the missing value for SS_total?
$$\begin{array} { l c c c c } \text { Source } & S S & d f & M S & \\\text { Between } & 20 & \mathrm { xx } & \mathrm { xx } & F = 5.00 \\\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \\\text { Total } & \mathrm { xx } & \mathrm { xx } & &\end{array}$$

A)22
B)30
C)54
D)74

Question 35

Which of the following describes a typical distribution of F-ratios?

A)Symmetrical with a mean of zero
B)Positively skewed with all values greater than or equal to zero
C)Negatively skewed with all values greater than or equal to zero
D)Symmetrical with a mean equal to $d f _ { \text {between } }$

Question 36

A researcher reports an F-ratio with df = 2,18 from an independent-measures research study.Based on the df values,how many treatments were compared in the study,and what was the total number of subjects participating in the study?

A)2 treatments and 19 subjects
B)2 treatments and 20 subjects
C)3 treatments and 21 subjects
D)3 treatments and 22 subjects

Question 37

An independent-measures research study compares three treatment conditions using a sample of n = 10 in each treatment.For this study,the three sample means are M₁ = 1,M₂ = 2,and M₃ = 3.For the ANOVA,what value would be obtained for $S S _ { \text {between } }$ ?

A)2
B)10
C)20
D)30

Question 38

In an analysis of variance,which of the following is not true?

A)SStotal = $S S _ { \text {between } }$ + $\text { SSwithin }$
B)dftotal = $d f _ { \text {between } }$ + $d f _ { \text {within } }$
C)MStotal = MSbetween + MSwithin
D)All three choices are true.

Question 39

For an analysis of variance comparing four treatment $M S _ { \text {between } }$ = 12.What is the value of $S S _ { \text {between } }$

A)3
B)4
C)36
D)48

Question 40

The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n = 11 participants in each treatment.Note that several values are missing in the table.What is the missing value for the F-ratio? $$\begin{array} { l r l r l } \text { Source } & S S & d f & M S \\\hline \text { Between } & \mathrm { xx } & \mathrm { xx } & 14 & F = \mathrm { xx } \\\text { Within } & \mathrm { xx } & \mathrm { xx } & \mathrm { xx } & \\\text { Total } & 154 & \mathrm { xx } &\end{array}$$

A)2
B)7
C)14
D)28

Question 41

For an analysis of variance comparing four treatment means with a separate sample of n = 8 participants in each treatment,the F-ratio will have df = 3,31.

Question 42

In an analysis of variance,which of the following is determined by the size of the sample variances?

A) $S S _ { \text {between } }$
B) $\text { SSwithin }$
C) $d f _ { \text {between } }$
D) $d f _ { \text {within } }$

Question 43

If an analysis of variance is used for the following data,what would be the effect of changing the value of M₂ to 25?
Sample Data
$$\begin{array} { l l } M _ { 1 } = 10 & M _ { 2 } = 20 \\S S _ { 1 } = 90 & S S _ { 2 } = 70\end{array}$$

A)Increase $S S _ { \text {between } }$ and increase the F-ratio
B)Increase $S S _ { \text {between } }$ and decrease the F-ratio
C)Decrease $S S _ { \text {between } }$ and increase the F-ratio
D)Decrease $S S _ { \text {between } }$ and decrease the F-ratio

Question 44

What is the purpose of posttests?

A)To determine whether a Type I error was committed
B)To determine how much difference exists between the treatments
C)To determine which treatments are significantly different
D)None of these

Question 45

A researcher uses an ANOVA to evaluate the mean difference between two treatments and obtains F(1,22)= 4.00.If the researcher had used an independent-measures t test to evaluate the data,what t value would be obtained?

A)t(22) = 2.00
B)t(22) = 16.00
C)t(23) = 2.00
D)t(23) = 16.00

Question 46

A research report concludes that there are significant differences among treatments,with "F(2,24)= 8.62,p < .01." If the same number of participants was used in each of the treatment conditions,then how many individuals were in each treatment?

A)7
B)9
C)10
D)30

Question 47

For an analysis of variance comparing three treatment means with a separate sample of n = 10 participants in each treatment,dfₜₒₜₐₗ = 29.

Question 48

The following table shows the results of an analysis of variance comparing three treatments.What is the value of ²,the percentage of variance accounted for,for these data?
$$\begin{array} { l r r r r } \text { Source } & S S & d f & M S & \\\text { Between } & 30 & 2 & 15 & F = 7.50 \\\text { Within } & 60 & 30 & 2 & \\\text { Total } & 90 & 32 & &\end{array}$$

A)30/60 = .5
B)30/90 = .33
C)60/90 = .67
D)2/30 = .067

Question 49

If an analysis of variance is used for the following data,what would be the effect of changing the value of SS1 to 50?

A)Increase $\text { SSwithin }$ and increase the size of the F-ratio M1 = 10 M2 = 20
B)Increase $\text { SSwithin }$ and decrease the size of the F-ratio SS1 = 90 SS2 = 70
C)Decrease $\text { SSwithin }$ and increase the size of the F-ratio
D)Decrease $\text { SSwithin }$ and decrease the size of the F-ratio

Question 50

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment.If the data produce an F-ratio of F = 4.60,which of the following is the correct statistical decision?

A)Reject the null hypothesis with α = .05 but not with α = .01
B)Reject the null hypothesis with either α = .05 or α = .01
C)Fail to reject the null hypothesis with either α = .05 or α = .01
D)There is not enough information to make a statistical decision

Question 51

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12)= 4.00.If the researcher had used an ANOVA to evaluate the data,what F-ratio would be obtained?

A)F(1, 12) = 2.00
B)F(1, 12) = 16.00
C)F(1, 11) = 2.00
D)F(1, 11) = 16.00

Question 52

For an independent-measures ANOVA comparing four treatment conditions,df between = 3.

Question 53

For an ANOVA,when the null hypothesis is true,the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.

Question 54

F-ratios are always greater than or equal to zero.

Question 55

If an analysis of variance produces $S S _ { \text {between } }$ treatments = 30 and t $M S _ { \text {between } }$ treatments = 10,then the ANOVA is comparing four treatment conditions.

Question 56

An F-ratio near 1.00 is an indication that the null hypothesis is likely to be true.

Question 57

For an independent-measures ANOVA with n = 10 participants in each treatment condition,dfwᵢthᵢn = 9.

Question 58

In general,what factors are most likely to reject the null hypothesis for an ANOVA?

A)Small mean differences and small variances
B)Small mean differences and large variances
C)Large mean differences and small variances
D)Large mean differences and large variances

Question 59

In an analysis of variance,MS_total = t $M S _ { \text {between } }$ + MS_within.

Question 60

For an analysis of variance comparing three treatment means,H₀ states that all three population means are the same and H₁ states that all three population means are different.

Question 61

Posttests are only needed if H₀ is rejected in an ANOVA comparing more than two treatments.

Question 62

The distribution of F-ratios is negatively skewed.

Question 63

In analysis of variance,large sample variances reduce the likelihood of rejecting the null hypothesis.

Question 64

After an ANOVA,a researcher computes ² to evaluate effect size and obtains11eedb96_7b94_556d_a0ba_3d9dc406b78d_TB2285_11² = 0.50.If the ANOVA had SS_total = 100,then $\text { SSwithin }$ = $S S _ { \text {between } }$ = 50.

Question 65

An ANOVA is used to determine whether any significant difference exists between treatment means,and posttests are used to determine exactly which treatment means are significantly different.

Question 66

If an analysis of variance produces a value of F = 0,then all the samples have the same mean.

Question 67

If an analysis of variance produces a value of F = 1.00,then all the samples have the same mean.

Question 68

$\text { SSwithin }$ measures the size of the sample variances.

Question 69

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments.If the t statistic has df = 12,then an ANOVA evaluating the same data would produce an F-ratio with df = 1,11.

Question 70

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study used a total of 31 participants.

Question 71

Effect size for analysis of variance is measured by ²,which equals $S S _ { \text {between } }$ divided by $\text { SSwithin }$ .

Question 72

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.If all the samples were the same size,then each sample had n = 7 participants.

Question 73

A researcher conducts an ANOVA to evaluate the mean difference between two treatments using the data from an independent-measures study and obtains F = 4.00.If the researcher had used an independent-measures t test,then t would be t = 2.00.

Question 74

An ANOVA comparing two treatment conditions produces $\text { SSwithin }$ = 80 and $S S _ { \text {between } }$ = 50.For these data,²= 25/80.

Question 75

The larger the differences among the sample means,the larger the numerator of the F-ratio will be.

Question 76

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study compared three treatments.

Question 77

$S S _ { \text {between } }$ measures the size of the mean differences from one treatment to another.

Question 78

Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.

Question 79

If an analysis of variance produces $S S _ { \text {between } }$ = 20 and $\text { SSwithin }$ = 40,then ² = 0.50.

Question 80

For an ANOVA,if $S S _ { \text {between } }$ = 40 and $\text { SSwithin }$ = 60,then ² = 40/100.